protected override EstimationResult BuildEstimate(Scalar spotPrice, CurveMarketData interestDataSet, CallPriceMarketData callDataSet, EquityCalibrationData equityCalData, SolutionInfo solution)
{
string[] names = new string[] { "S0", "kappa", "theta", "sigma",
"rho", "V0", "r", "q" };
Vector param = new Vector(8);
param[0] = spotPrice.Value;
param[Range.New(1, 5)] = solution.x[Range.New(0, 4)];
param[6] = equityCalData.zrFunc.Evaluate(TheoreticalModelsSettings.ConstantDYRFMaturity);
if (impliedDividends)
{
param[7] = solution.x[Range.End];// equityCalData.dyFunc.Evaluate(TheoreticalModelsSettings.ConstantDYRFMaturity);
}
else
{
param[7] = DY(equityCalData);
}
var result = new EstimationResult(names, param);
result.Fit = HestonCallOptimizationProblem.avgPricingError;
Console.WriteLine(result);
return(result);
}
protected override EstimationResult BuildEstimate(Scalar spotPrice, CurveMarketData interestDataSet, CallPriceMarketData callDataSet, EquityCalibrationData equityCalData, SolutionInfo solution)
{
string[] names = new string[] { "S0", "kappa", "theta", "sigma",
"rho", "V0", "r", "q" };
Vector param = new Vector(8);
param[0] = spotPrice.Value;
param[Range.New(1, 5)] = solution.x[Range.New(0, 4)];
param[6] = equityCalData.zrFunc.Evaluate(TheoreticalModelsSettings.ConstantDYRFMaturity);
if (impliedDividends)
param[7] = solution.x[Range.End];// equityCalData.dyFunc.Evaluate(TheoreticalModelsSettings.ConstantDYRFMaturity);
else
param[7] = DY(equityCalData);
var result = new EstimationResult(names, param);
result.Fit = HestonCallOptimizationProblem.avgPricingError;
Console.WriteLine(result);
return result;
}
private static void AssertEstimationResultsAreEqual(EstimationResult expected, EstimationResult actual)
{
if (expected == null)
{
Assert.IsNull(actual);
}
else
{
Assert.AreEqual(expected.Count, actual.Count);
foreach (var expectedItem in expected)
{
var actualItem = actual.Single(i => i.Key.Name == expectedItem.Key.Name);
AssertObserversAreEqual(expectedItem.Key, actualItem.Key, true);
Assert.AreEqual(expectedItem.Value, actualItem.Value);
}
}
}
/// <summary>
/// Attempts a calibration through <see cref="PelsserCappletOptimizationProblem"/>
/// using caps matrices.
/// </summary>
/// <param name="data">The data to be used in order to perform the calibration.</param>
/// <param name="settings">The parameter is not used.</param>
/// <param name="controller">The controller which may be used to cancel the process.</param>
/// <returns>The results of the calibration.</returns>
public EstimationResult Estimate(List <object> data, IEstimationSettings settings = null, IController controller = null, Dictionary <string, object> properties = null)
{
InterestRateMarketData dataset = data[0] as InterestRateMarketData;
MatrixMarketData normalVol = null;
if (data.Count > 1)
{
normalVol = (MatrixMarketData)data[1];
}
EstimationResult result;
if ((dataset.ZRMarket == null) || (dataset.CapVolatility == null))
{
result = new EstimationResult();
result.ErrorMessage = "Not enough data to calibrate.\n" +
"The estimator needs a ZRMarket and a CapVolatility " +
"defined inside InterestRateMarketData";
return(result);
}
// Backup the dates
DateTime effectiveDate = DateTime.Now.Date;
DateTime valuationDate = DateTime.Now.Date;
if (Document.ActiveDocument != null)
{
effectiveDate = Document.ActiveDocument.ContractDate;
valuationDate = Document.ActiveDocument.SimulationStartDate;
}
// Creates the Context.
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
Function zr = new PFunction(null);
zr.VarName = "zr";
// Load the zr.
double[,] zrvalue = (double[, ])ArrayHelper.Concat(dataset.ZRMarketDates.ToArray(), dataset.ZRMarket.ToArray());
zr.Expr = zrvalue;
prj.Symbols.Add(zr);
var bm = BlackModelFactory(zr);
if (bm is BachelierNormalModel)
{
(bm as BachelierNormalModel).Tenor = dataset.CapTenor;
}
double deltak = dataset.CapTenor;
Matrix capVol = normalVol != null ? normalVol.Values:dataset.CapVolatility;
Vector capMat = normalVol != null ? normalVol.RowValues: dataset.CapMaturity;
Vector capK = normalVol != null ? normalVol.ColumnValues: dataset.CapRate;
var preferences = settings as Fairmat.Calibration.CapVolatilityFiltering;
// Matrix calculated with black.
var blackCaps = new Matrix(capMat.Length, capK.Length);
for (int m = 0; m < capMat.Length; m++)
{
for (int s = 0; s < capK.Length; s++)
{
bool skip = false;
if (preferences != null)
{
if (capK[s] < preferences.MinCapRate || capK[s] > preferences.MaxCapRate ||
capMat[m] < preferences.MinCapMaturity || capMat[m] > preferences.MaxCapMaturity)
{
skip = true;
}
}
if (capVol[m, s] == 0 || skip)
{
blackCaps[m, s] = 0;
}
else
{
blackCaps[m, s] = bm.Cap(capK[s], capVol[m, s], deltak, capMat[m]);
}
}
}
if (blackCaps.IsNaN())
{
Console.WriteLine("Black caps matrix has non real values:");
Console.WriteLine(blackCaps);
throw new Exception("Cannot calculate Black caps");
}
// Maturity goes from 0 to the last item with step deltaK.
Vector maturity = new Vector((int)(1.0 + capMat[capMat.Length - 1] / deltak));
for (int l = 0; l < maturity.Length; l++)
{
maturity[l] = deltak * l;
}
Vector fwd = new Vector(maturity.Length - 1);
for (int i = 0; i < fwd.Length; i++)
{
fwd[i] = bm.Fk(maturity[i + 1], deltak);
}
// Creates a default Pelsser model.
Pelsser.SquaredGaussianModel model = new Pelsser.SquaredGaussianModel();
model.a1 = (ModelParameter)0.014;
model.sigma1 = (ModelParameter)0.001;
model.zr = (ModelParameter)"@zr";
StochasticProcessExtendible iex = new StochasticProcessExtendible(prj, model);
prj.Processes.AddProcess(iex);
prj.Parse();
DateTime t0 = DateTime.Now;
Caplet cp = new Caplet();
PelsserCappletOptimizationProblem problem = new PelsserCappletOptimizationProblem(prj, cp, maturity, fwd, capK, deltak, capMat, blackCaps);
IOptimizationAlgorithm solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 35;
o.TargetCost = 0.0025;
o.MaxIter = 10;
o.Verbosity = Math.Max(1, Engine.Verbose);
o.controller = controller;
// Parallel evaluation is not supported for this calibration.
o.Parallel = false;
o.Debug = true;
SolutionInfo solution = null;
Vector x0 = (Vector) new double[] { 0.1, 0.1 };
solution = solver.Minimize(problem, o, x0);
if (solution.errors)
{
return(new EstimationResult(solution.message));
}
o.epsilon = 10e-7;
o.h = 10e-7;
o.MaxIter = 1000;
o.Debug = true;
o.Verbosity = Math.Max(1, Engine.Verbose);
if (solution != null)
{
solution = solver2.Minimize(problem, o, solution.x);
}
else
{
solution = solver2.Minimize(problem, o, x0);
}
if (solution.errors)
{
return(new EstimationResult(solution.message));
}
Console.WriteLine(solution);
string[] names = new string[] { "alpha1", "sigma1" };
result = new EstimationResult(names, solution.x);
result.ZRX = (double[])dataset.ZRMarketDates.ToArray();
result.ZRY = (double[])dataset.ZRMarket.ToArray();
result.Objects = new object[1];
result.Objects[0] = solution.obj;
//result.Fit = solution.obj;//Uncomment in 1.6
// Restore the dates
if (Document.ActiveDocument != null)
{
Document.ActiveDocument.ContractDate = effectiveDate;
Document.ActiveDocument.SimulationStartDate = valuationDate;
}
return(result);
}
/// <summary>
/// Populate editable fields from name and value vectors
/// specific to the Heston extended process.
/// </summary>
/// <param name="stocProcess">
/// The stochastic process which is being referenced to.
/// </param>
/// <param name="estimate">
/// The estimation result which contains values and names of parameters.
/// It will be searched for S0, kappa, theta, sigma, V0, r, q and rho.
/// </param>
public void Populate(IStochasticProcess stocProcess, EstimationResult estimate)
{
bool found;
this.S0 = new ModelParameter(PopulateHelper.GetValue("S0", estimate.Names, estimate.Values, out found), this.S0.Description);
this.k = new ModelParameter(PopulateHelper.GetValue("kappa", estimate.Names, estimate.Values, out found), this.k.Description);
this.theta = new ModelParameter(PopulateHelper.GetValue("theta", estimate.Names, estimate.Values, out found), this.theta.Description);
this.sigma = new ModelParameter(PopulateHelper.GetValue("sigma", estimate.Names, estimate.Values, out found), this.sigma.Description);
this.V0 = new ModelParameter(PopulateHelper.GetValue("V0", estimate.Names, estimate.Values, out found), this.V0.Description);
this.r = new ModelParameter(PopulateHelper.GetValue("r", estimate.Names, estimate.Values, out found), this.r.Description);
this.q = new ModelParameter(PopulateHelper.GetValue("q", estimate.Names, estimate.Values, out found), this.q.Description);
int index = stocProcess.NoiseIndex;
ProjectProcess prj = stocProcess.Context as ProjectProcess;
// Updates the correlation.
prj.Processes.r.Set(index, index + 1, (RightValue)PopulateHelper.GetValue("rho", estimate.Names, estimate.Values, out found));
}
/// <summary>
/// Attempts to solve the Variance Gamma Optimization problem using
/// <see cref="Heston.VarianceGammaOptimizationProblem"/>.
/// </summary>
/// <param name="data">
/// The data to be used in order to perform the optimization.
/// </param>
/// <param name="settings">The parameter is not used.</param>
/// <returns>The results of the optimization.</returns>
public EstimationResult Estimate(List<object> data, IEstimationSettings settings = null, IController controller = null, Dictionary<string, object> properties = null)
{
EquitySpotMarketData espmd = data[0] as EquitySpotMarketData;
CallPriceMarketData cpmd = data[1] as CallPriceMarketData;
DiscountingCurveMarketData dcmd = data[2] as DiscountingCurveMarketData;
EquityCalibrationData ecd = new EquityCalibrationData(cpmd, dcmd);
this.s0 = espmd.Price;
this.r = espmd.RiskFreeRate;
this.q = espmd.DividendYield;
this.k = ecd.Hdata.Strike;
this.m = ecd.Hdata.Maturity;
this.cp = ecd.Hdata.CallPrice;
Vector x0 = (Vector)new double[] { -0.1, 0.2, 0.1 };
IOptimizationAlgorithm algorithm = new QADE();
OptimizationSettings optimizationSettings = new DESettings();
// Maximum number of iteration allowed.
// Positive integer values print debug info.
optimizationSettings.Verbosity = 1;
// Tolerance.
optimizationSettings.epsilon = 10e-5;
var solution = algorithm.Minimize(new VarianceGammaOptimizationProblem(this.q, this.s0, this.k,
this.r, this.cp, this.m),
optimizationSettings, x0);
if (solution.errors)
return new EstimationResult(solution.message);
var er = new EstimationResult();
er.Names= new string[]{"S0","theta","sigma","nu","rate","dividend"};
er.Values = new double[] {this.s0,solution.x[0],solution.x[1],solution.x[2],this.r,this.q};
return er;
}
/// <summary>
/// Attempts a calibration through <see cref="CapsHW1OptimizationProblem"/>
/// using caps matrices.
/// </summary>
/// <param name="data">The data to be used in order to perform the calibration.</param>
/// <param name="settings">The parameter is not used.</param>
/// <param name="controller">The controller which may be used to cancel the process.</param>
/// <returns>The results of the calibration.</returns>
public EstimationResult Estimate(List <object> data, IEstimationSettings settings = null, IController controller = null, Dictionary <string, object> properties = null)
{
InterestRateMarketData dataset = data[0] as InterestRateMarketData;
PFunction zr = new PFunction(null);
zr.VarName = "zr";
var preferences = settings as Fairmat.Calibration.CapVolatilityFiltering;
// Loads ZR
double[,] zrvalue = (double[, ])ArrayHelper.Concat(dataset.ZRMarketDates.ToArray(), dataset.ZRMarket.ToArray());
zr.Expr = zrvalue;
BlackModel bm = new BlackModel(zr);
double deltak = dataset.CapTenor;
if (dataset.CapVolatility == null)
{
return(new EstimationResult("Cap not available at requested date"));
}
Matrix capVolatility = dataset.CapVolatility;
Vector capMaturity = dataset.CapMaturity;
Vector capRate = dataset.CapRate;
double a = 0.1;
double sigma = 0.1;
// Matrix calculated with Black.
Matrix blackCaps = new Matrix(capMaturity.Length, capRate.Length);
Matrix logic = new Matrix(capMaturity.Length, capRate.Length);
for (int m = 0; m < capMaturity.Length; m++)
{
for (int s = 0; s < capRate.Length; s++)
{
blackCaps[m, s] = bm.Cap(capRate[s], capVolatility[m, s], deltak, capMaturity[m]);
if (double.IsNaN(blackCaps[m, s]))
{
bm.Cap(capRate[s], capVolatility[m, s], deltak, capMaturity[m]);
throw new Exception("Malformed black caps");
}
if (blackCaps[m, s] == 0.0)
{
logic[m, s] = 0.0;
}
else
{
logic[m, s] = 1.0;
}
//filter
if (preferences != null)
{
if (capRate[s] < preferences.MinCapRate || capRate[s] > preferences.MaxCapRate ||
capMaturity[m] < preferences.MinCapMaturity || capMaturity[m] > preferences.MaxCapMaturity)
{
logic[m, s] = 0; blackCaps[m, s] = 0;
}
}
}
}
DateTime t0 = DateTime.Now;
CapHW1 hw1Caps = new CapHW1(zr);
Matrix caps = hw1Caps.HWMatrixCaps(capMaturity, capRate, a, sigma, deltak);
for (int m = 0; m < capMaturity.Length; m++)
{
for (int s = 0; s < capRate.Length; s++)
{
caps[m, s] = logic[m, s] * caps[m, s];
}
}
CapsHW1OptimizationProblem problem = new CapsHW1OptimizationProblem(hw1Caps, blackCaps, capMaturity, capRate, deltak);
Vector provaparam = new Vector(2);
var solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 20;
o.MaxIter = 10;
o.Verbosity = 1;
o.Parallel = false;
SolutionInfo solution = null;
Vector x0 = new Vector(new double[] { 0.05, 0.01 });
o.controller = controller;
solution = solver.Minimize(problem, o, x0);
o.epsilon = 10e-8;
o.h = 10e-8;
o.MaxIter = 100;
solution = solver2.Minimize(problem, o, solution.x);
if (solution.errors)
{
return(new EstimationResult(solution.message));
}
Console.WriteLine("Solution:");
Console.WriteLine(solution);
string[] names = new string[] { "Alpha", "Sigma" };
//solution.x[0] *= 3;
EstimationResult result = new EstimationResult(names, solution.x);
result.ZRX = (double[])dataset.ZRMarketDates.ToArray();
result.ZRY = (double[])dataset.ZRMarket.ToArray();
return(result);
}
public static void AddCount(this StringBuilder builder, GeometryType type, EstimationResult result, string separator)
{
builder.Append(result.GetCount(type));
builder.Append(separator);
}
/// <summary>
/// Attempts a calibration through <see cref="CapsCIROptimizationProblem"/>
/// using caps matrices.
/// </summary>
/// <param name="data">The data to be used in order to perform the calibration.</param>
/// <param name="settings">The parameter is not used.</param>
/// <param name="controller">A controller used for the optimization process.</param>
/// <returns>The results of the calibration.</returns>
public EstimationResult Estimate(List <object> data, IEstimationSettings settings = null, IController controller = null, Dictionary <string, object> properties = null)
{
InterestRateMarketData dataset = data[0] as InterestRateMarketData;
// Creates the context.
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
CapCIROptimizationProblem problem = new CapCIROptimizationProblem(dataset);
IOptimizationAlgorithm solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 50;
o.MaxIter = 50;
o.Verbosity = 1;
o.Parallel = false;
o.controller = controller;
SolutionInfo solution = null;
Vector x0 = new Vector(new double[] { 1, 0.01, 0.05 });
solution = solver.Minimize(problem, o, x0);
if (solution.errors)
{
return(new EstimationResult(solution.message));
}
o.epsilon = 10e-10;
o.h = 10e-10;
o.MaxIter = 1000;
if (solution != null)
{
solution = solver2.Minimize(problem, o, solution.x);
}
else
{
solution = solver2.Minimize(problem, o, x0);
}
if (solution.errors)
{
return(new EstimationResult(solution.message));
}
Console.WriteLine("Solution:");
Console.WriteLine(solution);
string[] names = CIR.parameterNames;
Vector values = new Vector(4);
values[Range.New(0, 2)] = solution.x;
values[3] = problem.r0;
EstimationResult result = new EstimationResult(names, values);
return(result);
}
public override AquisitionFunctionValue GetAquistionValue(EstimationResult er)
{
return(new AquisitionFunctionValue(er.X, er.UpperBound - er.LowerBound));
}
/// <summary>
/// Populate editable fields from name and value vectors
/// specific to the CIR process.
/// </summary>
/// <param name="container">
/// The stochastic process which is being referenced to.
/// </param>
/// <param name="estimate">
/// The estimation result which contains values and names of parameters.
/// </param>
public void Populate(IStochasticProcess container, EstimationResult estimate)
{
bool found;
this.parameterValues = new double[4];
for (int i = 0; i < parameterNames.Length; i++)
{
this.parameterValues[i] = PopulateHelper.GetValue(parameterNames[i],
estimate.Names, estimate.Values,
out found);
Console.WriteLine("ParameterValues[{0}] = {1}\t ParameterNames[{0}] = {2}",
i, this.parameterValues[i], parameterNames[i]);
}
SetParametersValue();
}
/*
/// <summary>
/// Populate editable fields from name and value vectors
/// specific to HW.
/// </summary>
/// <param name="names">
/// An array with the names of the variable,
/// will search for alpha (or a1), sigma (or sigma1).
/// </param>
/// <param name="values">The values associated to the parameters in names.</param>
public void Populate(string[] names, double[] values)
{
bool found = false;
this.alpha1 = new ModelParameter(PopulateHelper.GetValue("alpha", "a1", names, values, out found), alphaDescription);
this.sigma1 = new ModelParameter(PopulateHelper.GetValue("sigma", "sigma1", names, values, out found), sigmaDescription);
this.lambda0 = new ModelParameter(PopulateHelper.GetValue("Lambda0", "lambda0", names, values, out found), lambda0Description);
}
*/
/// <summary>
/// Populate editable fields from name and value vectors
/// specific to the Heston extended process.
/// </summary>
/// <param name="stocProcess">
/// The stochastic process which is being referenced to.
/// </param>
/// <param name="estimate">
/// The estimation result which contains values and names of parameters.
/// It will be searched for S0, kappa, theta, sigma, V0 and rho.
/// </param>
public void Populate(IStochasticProcess stocProcess, EstimationResult estimate)
{
bool found;
this.alpha1 = new ModelParameter(PopulateHelper.GetValue("alpha", "a1", estimate.Names, estimate.Values, out found), alphaDescription);
this.sigma1 = new ModelParameter(PopulateHelper.GetValue("sigma", "sigma1", estimate.Names, estimate.Values, out found), sigmaDescription);
this.lambda0 = new ModelParameter(PopulateHelper.GetValue("Lambda0", "lambda0", estimate.Names, estimate.Values, out found), lambda0Description);
}
public abstract AquisitionFunctionValue GetAquistionValue(EstimationResult er);
private EstimationResult QuantLibEstimate(CurveMarketData discoutingCurve, CallPriceMarketData Hdataset)
{
EquityCalibrationData HCalData = new EquityCalibrationData(Hdataset, discoutingCurve);
bool hasArbitrage = HCalData.HasArbitrageOpportunity(10e-2);
if (hasArbitrage)
{
Console.WriteLine("Market data contains arbitrage opportunity");
}
this.r = new DVPLDOM.PFunction(discoutingCurve.Durations, discoutingCurve.Values);
this.q = HCalData.dyFunc as PFunction;
//this.r.Parse(null);
//this.q.Parse(null);
Hdataset.Volatility = new Matrix(Hdataset.CallPrice.R, Hdataset.CallPrice.C);
for (int i = 0; i < Hdataset.Volatility.R; i++)
{
double m = Hdataset.Maturity[i];
for (int j = 0; j < Hdataset.Volatility.C; j++)
{
if (Hdataset.CallPrice[i, j] > 0)
{
var bs = new Fairmat.Finance.BlackScholes(r.Evaluate(m), Hdataset.S0, Hdataset.Strike[j], 0, m, q.Evaluate(m));
//Hdataset.Volatility[i, j] = Hdataset.Volatility[i, j] * Hdataset.Volatility[i, j] * Hdataset.Maturity[i];
//Hdataset.Volatility[i, j] = bs.ImpliedCallVolatility(Hdataset.CallPrice[i, j]);
}
}
}
Console.WriteLine(Hdataset.Volatility);
IFunction impVol = FitImplVolModel(Hdataset);
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
prj.Symbols.Add(impVol);
// doc.WriteToXMLFile("impVol.fair");
int nmat = calibrationSettings.LocalVolatilityMaturities;
int nstrike = calibrationSettings.LocalVolatilityStrikes;
double lastMat = Hdataset.Maturity[SymbolicIntervalExtremes.End];
double lastStr = Hdataset.Strike[SymbolicIntervalExtremes.End];
Vector locVolMat = Vector.Linspace(Hdataset.Maturity[0], lastMat, nmat);
Vector locVolStr = Vector.Linspace(Hdataset.Strike[0], lastStr, nstrike);
Matrix locVolMatrix = new Matrix(nmat, nstrike);
double t, dt, forwardValue, y, dy, strike, strikep, strikem, w, wp, wm, dwdy;
double d2wdy2, den1, den2, den3, strikept, strikemt, wpt, wmt, dwdt;
Integrate integrate = new Integrate(this);
for (int i = 0; i < nmat; i++)
{
t = locVolMat[i];
forwardValue = Hdataset.S0 * Math.Exp(integrate.AdaptLobatto(0.0, t));
for (int j = 0; j < nstrike; j++)
{
strike = locVolStr[j];
y = Math.Log(strike / forwardValue);
dy = ((Math.Abs(y) > 0.001) ? y * 0.0001 : 0.000001);
// strike derivative
strikep = strike * Math.Exp(dy);
strikem = strike / Math.Exp(dy);
w = impVol.Evaluate(t, strike);
wp = impVol.Evaluate(t, strikep);
wm = impVol.Evaluate(t, strikem);
dwdy = (wp - wm) / (2.0 * dy);
d2wdy2 = (wp - 2.0 * w + wm) / (dy * dy);
// time derivative
if (t == 0.0)
{
dt = 0.0001;
strikept = strike * Math.Exp(integrate.AdaptLobatto(0.0, t + dt));
wpt = impVol.Evaluate(t + dt, strikept);
// if (wpt < w)
// Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t, t + dt);
dwdt = (wpt - w) / dt;
}
else
{
dt = Math.Min(0.0001, t / 2.0);
strikept = strike * Math.Exp(integrate.AdaptLobatto(t, t + dt));
strikemt = strike * Math.Exp(-integrate.AdaptLobatto(t - dt, t));
wpt = impVol.Evaluate(t + dt, strikept);
wmt = impVol.Evaluate(t + dt, strikemt);
//if (wpt < w)
// Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t, t + dt);
//if (w < wmt)
// Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t-dt, t);
dwdt = (wpt - wmt) / (2.0 * dt);
}
if (dwdy == 0.0 && d2wdy2 == 0.0)
{
locVolMatrix[i, j] = Math.Sqrt(dwdt);
}
else
{
den1 = 1.0 - y / w * dwdy;
den2 = 0.25 * (-0.25 - 1.0 / w + y * y / w / w) * dwdy * dwdy;
den3 = 0.5 * d2wdy2;
locVolMatrix[i, j] = dwdt / (den1 + den2 + den3);
//if (locVolMatrix[i,j] < 0.0)
// Console.WriteLine("Negative local vol^2 at strike {0} and time {1}; " +
// "Black vol surface is not smooth enought.", strike, t);
}
}
}
// Create dupire outputs.
Console.WriteLine(locVolMat);
PFunction2D.PFunction2D localVol = new PFunction2D.PFunction2D(locVolMat, locVolStr, locVolMatrix);
localVol.Parse(null);
string[] names = new string[] { "S0" };
Vector param = new Vector(1);
param[0] = Hdataset.S0;
EstimationResult result = new EstimationResult(names, param);
//result.Objects = new object[3];
result.Objects = new object[4];
result.Objects[0] = this.r;
result.Objects[1] = this.q;
result.Objects[2] = localVol;
result.Objects[3] = impVol;
//Console.WriteLine("r = " + HCalData.Rate.ToString());
//Console.WriteLine("q = " + HCalData.DividendYield.ToString());
return(result);
}
/// <summary>
/// Populate editable fields from name and value vectors
/// specific to the Heston extended process.
/// </summary>
/// <param name="stocProcess">
/// The stochastic process which is being referenced to.
/// </param>
/// <param name="estimate">
/// The estimation result which contains values and names of parameters.
/// It will be searched for S0, kappa, theta, sigma, V0 and rho.
/// </param>
public void Populate(IStochasticProcess stocProcess, EstimationResult estimate)
{
bool found;
this.S0 = new ModelParameter(PopulateHelper.GetValue("S0", estimate.Names, estimate.Values, out found), this.S0.Description);
this.k = new ModelParameter(PopulateHelper.GetValue("kappa", estimate.Names, estimate.Values, out found), this.k.Description);
this.theta = new ModelParameter(PopulateHelper.GetValue("theta", estimate.Names, estimate.Values, out found), this.theta.Description);
this.sigma = new ModelParameter(PopulateHelper.GetValue("sigma", estimate.Names, estimate.Values, out found), this.sigma.Description);
this.V0 = new ModelParameter(PopulateHelper.GetValue("V0", estimate.Names, estimate.Values, out found), this.V0.Description);
int index = stocProcess.NoiseIndex;
ProjectProcess prj = stocProcess.Context as ProjectProcess;
// Update the correlation matrix.
prj.Processes.r.Set(index, index + 1, (RightValue)PopulateHelper.GetValue("rho", estimate.Names, estimate.Values, out found));
bool errors = RetrieveCurve(stocProcess.Context, false);
if (!errors)
{
this.zrCurve.Expr = (estimate.Objects[0] as Matrix).ToArray();
this.dyCurve.Expr = (estimate.Objects[1] as Matrix).ToArray();
//Calibrator assumes dividend yield is a step constant function, the simulation model must be coherent with that assumption.
(this.dyCurve as PFunction).m_Function.iType = DVPLUtils.EInterpolationType.ZERO_ORDER_LEFT;
}
}
/// <summary>
/// Attempts a calibration through <see cref="SwaptionHW1OptimizationProblem"/>
/// using swaption matrices.
/// </summary>
/// <param name="data">The data to be used in order to perform the calibration.</param>
/// <param name="settings">The parameter is not used.</param>
/// <param name="controller">The controller which may be used to cancel the process.</param>
/// <returns>The results of the calibration.</returns>
public EstimationResult Estimate(List<object> data, IEstimationSettings settings = null, IController controller = null, Dictionary<string, object> properties = null)
{
InterestRateMarketData dataset = data[0] as InterestRateMarketData;
PFunction zr = new PFunction(null);
// Loads the zero rate.
double[,] zrvalue = (double[,])ArrayHelper.Concat(dataset.ZRMarketDates.ToArray(), dataset.ZRMarket.ToArray());
zr.Expr = zrvalue;
double deltak = dataset.SwaptionTenor;
var swaptionsFiltering = settings as SwaptionsFiltering;
if (swaptionsFiltering == null)
swaptionsFiltering = new SwaptionsFiltering();//creates a default
int maturitiesCount = dataset.OptionMaturity.Count(x => x >= swaptionsFiltering.MinSwaptionMaturity && x <= swaptionsFiltering.MaxSwaptionMaturity);
int durationsCount = dataset.SwapDuration.Count(x => x >= swaptionsFiltering.MinSwapDuration && x <= swaptionsFiltering.MaxSwapDuration);
Console.WriteLine(string.Format("Calibrating on {0} swaptions prices [#maturiries x #durations]=[{1} x {2}]", maturitiesCount * durationsCount, maturitiesCount,durationsCount));
if (maturitiesCount * durationsCount == 0)
return new EstimationResult("No swaptions satisfying criteria found, please relax filters");
Matrix swaptionsVolatility = new Matrix(maturitiesCount, durationsCount);// dataset.SwaptionsVolatility;
Vector optionMaturity = new Vector(maturitiesCount);// dataset.OptionMaturity;
Vector swapDuration = new Vector(durationsCount);// dataset.SwapDuration;
//Build filtered matrix and vectors
int fm=0;
for (int m = 0; m < dataset.OptionMaturity.Length; m++)
{
int fd=0;
if (dataset.OptionMaturity[m] >= swaptionsFiltering.MinSwaptionMaturity && dataset.OptionMaturity[m] <= swaptionsFiltering.MaxSwaptionMaturity)
{
for (int d = 0; d < dataset.SwapDuration.Length; d++)
{
if (dataset.SwapDuration[d] >= swaptionsFiltering.MinSwapDuration && dataset.SwapDuration[d] <= swaptionsFiltering.MaxSwapDuration)
{
swaptionsVolatility[fm, fd] = dataset.SwaptionsVolatility[m, d];
swapDuration[fd] = dataset.SwapDuration[d];
fd++; }
}
optionMaturity[fm] = dataset.OptionMaturity[m];
fm++;
}
}
SwaptionsBlackModel swbm = new SwaptionsBlackModel(zr);
Matrix fsr;
var blackSwaptionPrice = 1000.0 * swbm.SwaptionsSurfBM(optionMaturity, swapDuration, swaptionsVolatility, deltak, out fsr);
Console.WriteLine("SwaptionHWEstimator: Black model prices");
Console.WriteLine(blackSwaptionPrice);
SwaptionHW1 swhw1 = new SwaptionHW1(zr);
SwaptionHW1OptimizationProblem problem = new SwaptionHW1OptimizationProblem(swhw1, blackSwaptionPrice, optionMaturity, swapDuration, deltak);
IOptimizationAlgorithm solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 20;
o.MaxIter = 5;
o.Verbosity = 1;
o.controller = controller;
SolutionInfo solution = null;
Vector x0 = new Vector(new double[] { 0.1, 0.1 });
solution = solver.Minimize(problem, o, x0);
if (solution.errors)
return new EstimationResult(solution.message);
o.epsilon = 10e-8;
o.h = 10e-8;
o.MaxIter = 1000;
// We can permit this, given it is fast.
o.accourate_numerical_derivatives = true;
if (solution != null)
solution = solver2.Minimize(problem, o, solution.x);
else
solution = solver2.Minimize(problem, o, x0);
if (solution.errors)
return new EstimationResult(solution.message);
Console.WriteLine("Solution:");
Console.WriteLine(solution);
string[] names = new string[] { "Alpha", "Sigma" };
EstimationResult result = new EstimationResult(names, solution.x);
result.ZRX = (double[])dataset.ZRMarketDates.ToArray();
result.ZRY = (double[])dataset.ZRMarket.ToArray();
double obj = problem.Obj(solution.x);
return result;
}
public EstimationResult Estimate(List<object> data, IEstimationSettings settings = null, IController controller = null, Dictionary<string, object> properties = null)
{
EstimationResult r = new EstimationResult();
r.Objects = new object[] { };
return r;
}
public void Constructor_Null_ArgumentNullException()
{
// Act
var result = new EstimationResult(null);
}
/// <summary>
/// Attempts a calibration through <see cref="CapsCIROptimizationProblem"/>
/// using caps matrices.
/// </summary>
/// <param name="data">The data to be used in order to perform the calibration.</param>
/// <param name="settings">The parameter is not used.</param>
/// <param name="controller">A controller used for the optimization process.</param>
/// <returns>The results of the calibration.</returns>
public EstimationResult Estimate(List<object> data, IEstimationSettings settings = null, IController controller = null, Dictionary<string, object> properties = null)
{
InterestRateMarketData dataset = data[0] as InterestRateMarketData;
// Creates the context.
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
CapCIROptimizationProblem problem = new CapCIROptimizationProblem(dataset);
IOptimizationAlgorithm solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 50;
o.MaxIter = 50;
o.Verbosity = 1;
o.Parallel = false;
o.controller = controller;
SolutionInfo solution = null;
Vector x0 = new Vector(new double[] { 1, 0.01, 0.05 });
solution = solver.Minimize(problem, o, x0);
if (solution.errors)
return new EstimationResult(solution.message);
o.epsilon = 10e-10;
o.h = 10e-10;
o.MaxIter = 1000;
if (solution != null)
solution = solver2.Minimize(problem, o, solution.x);
else
solution = solver2.Minimize(problem, o, x0);
if (solution.errors)
return new EstimationResult(solution.message);
Console.WriteLine("Solution:");
Console.WriteLine(solution);
string[] names = CIR.parameterNames;
Vector values = new Vector(4);
values[Range.New(0, 2)] = solution.x;
values[3] = problem.r0;
EstimationResult result = new EstimationResult(names, values);
return result;
}
/// <summary>
/// Attempts a calibration through <see cref="SwaptionHW1OptimizationProblem"/>
/// using swaption matrices.
/// </summary>
/// <param name="data">The data to be used in order to perform the calibration.</param>
/// <param name="settings">The parameter is not used.</param>
/// <param name="controller">The controller which may be used to cancel the process.</param>
/// <returns>The results of the calibration.</returns>
public EstimationResult Estimate(List<object> data, IEstimationSettings settings = null, IController controller = null, Dictionary<string, object> properties = null)
{
LambdaCalibrationSettings lsettings = (LambdaCalibrationSettings)settings;
if (lsettings.Years > lsettings.BondMaturity)
throw new Exception("Bond maturity has to be greater of the historical series time span.");
InterestRateMarketData irmd = data[0] as InterestRateMarketData;
List<object> IrmdData = new List<object>();
IrmdData.Add(irmd);
SwaptionHWEstimator shwe = new SwaptionHWEstimator();
EstimationResult er1 = shwe.Estimate(IrmdData);
DiscountingCurveMarketData[] dcmd = Array.ConvertAll<IMarketData, DiscountingCurveMarketData>
((IMarketData[])data[1], el => (DiscountingCurveMarketData)el);
MarketPriceOfRiskCalculator mporc = new MarketPriceOfRiskCalculator();
double lambda = mporc.Calculate(dcmd, lsettings);
string[] names = new string[er1.Names.Length + 1];
for (int i = 0; i < er1.Names.Length; i++)
names[i] = er1.Names[i];
names[er1.Names.Length] = "Lambda0";
Vector values = new Vector(er1.Values.Length + 1);
values[new Range(0, values.Length - 2)] = (Vector) er1.Values;
values[Range.End] = lambda;
EstimationResult result = new EstimationResult(names, values);
return result;
}
public EstimationResult Estimate(IDictionary <string, string> runtimeParameters, EstimationResult previousStageResult, bool optimize)
{
var result = new EstimationResult(previousStageResult);
var optimized = Enumerable.Empty <EstimationResult.ParameterValue>();
if (optimize)
{
optimized = Optimize();
if (previousStageResult != null && previousStageResult.Parameters != null && previousStageResult.Parameters.Count > 0)
{
result.Parameters.AddRange(optimized);
}
else
{
result.Parameters = optimized.ToList();
}
}
foreach (var runtimeParameter in runtimeParameters)
{
if (!_values.ContainsKey(runtimeParameter.Key))
{
_values.Add(runtimeParameter);
}
}
result.CalculationTime = ComputeTime(previousStageResult != null ? previousStageResult.Time : 0);
result.Parameters.AddRange(
GetParameters().Where(p => optimized.All(op => op.Name != p.Name)).
Select(p =>
new EstimationResult.ParameterValue {
Name = p.Name,
InitialValue = GetParameterValue(p.Name),
NewValue = GetParameterValue(p.Name)
})
);
foreach (var runtimeParameter in runtimeParameters)
{
_values.Remove(runtimeParameter.Key);
}
return(result);
}
/// <summary>
/// Attempts a calibration through <see cref="CapsHW1OptimizationProblem"/>
/// using caps matrices.
/// </summary>
/// <param name="data">The data to be used in order to perform the calibration.</param>
/// <param name="settings">The parameter is not used.</param>
/// <param name="controller">The controller which may be used to cancel the process.</param>
/// <returns>The results of the calibration.</returns>
public EstimationResult Estimate(List<object> data, IEstimationSettings settings = null, IController controller = null, Dictionary<string, object> properties = null)
{
InterestRateMarketData dataset = data[0] as InterestRateMarketData;
PFunction zr = new PFunction(null);
zr.VarName = "zr";
var preferences = settings as Fairmat.Calibration.CapVolatilityFiltering;
// Loads ZR
double[,] zrvalue = (double[,])ArrayHelper.Concat(dataset.ZRMarketDates.ToArray(), dataset.ZRMarket.ToArray());
zr.Expr = zrvalue;
BlackModel bm = new BlackModel(zr);
double deltak = dataset.CapTenor;
if (dataset.CapVolatility == null)
return new EstimationResult("Cap not available at requested date");
Matrix capVolatility = dataset.CapVolatility;
Vector capMaturity = dataset.CapMaturity;
Vector capRate = dataset.CapRate;
double a = 0.1;
double sigma = 0.1;
// Matrix calculated with Black.
Matrix blackCaps = new Matrix(capMaturity.Length, capRate.Length);
Matrix logic = new Matrix(capMaturity.Length, capRate.Length);
for (int m = 0; m < capMaturity.Length; m++)
{
for (int s = 0; s < capRate.Length; s++)
{
blackCaps[m, s] = bm.Cap(capRate[s], capVolatility[m, s], deltak, capMaturity[m]);
if (double.IsNaN(blackCaps[m, s]))
{
bm.Cap(capRate[s], capVolatility[m, s], deltak, capMaturity[m]);
throw new Exception("Malformed black caps");
}
if (blackCaps[m, s] == 0.0)
{
logic[m, s] = 0.0;
}
else
{
logic[m, s] = 1.0;
}
//filter
if (preferences != null)
{
if (capRate[s] < preferences.MinCapRate || capRate[s] > preferences.MaxCapRate ||
capMaturity[m]<preferences.MinCapMaturity|| capMaturity[m]>preferences.MaxCapMaturity)
{logic[m, s] = 0; blackCaps[m, s] = 0;}
}
}
}
DateTime t0 = DateTime.Now;
CapHW1 hw1Caps = new CapHW1(zr);
Matrix caps = hw1Caps.HWMatrixCaps(capMaturity, capRate, a, sigma, deltak);
for (int m = 0; m < capMaturity.Length; m++)
{
for (int s = 0; s < capRate.Length; s++)
{
caps[m, s] = logic[m, s] * caps[m, s];
}
}
CapsHW1OptimizationProblem problem = new CapsHW1OptimizationProblem(hw1Caps, blackCaps, capMaturity, capRate, deltak);
Vector provaparam = new Vector(2);
var solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 20;
o.MaxIter = 10;
o.Verbosity = 1;
o.Parallel = false;
SolutionInfo solution = null;
Vector x0 = new Vector(new double[] { 0.05, 0.01 });
o.controller = controller;
solution = solver.Minimize(problem, o, x0);
o.epsilon = 10e-8;
o.h = 10e-8;
o.MaxIter = 100;
solution = solver2.Minimize(problem, o, solution.x);
if (solution.errors)
return new EstimationResult(solution.message);
Console.WriteLine("Solution:");
Console.WriteLine(solution);
string[] names = new string[] { "Alpha", "Sigma" };
//solution.x[0] *= 3;
EstimationResult result = new EstimationResult(names, solution.x);
result.ZRX = (double[])dataset.ZRMarketDates.ToArray();
result.ZRY = (double[])dataset.ZRMarket.ToArray();
return result;
}
public void Populate(IStochasticProcess container, EstimationResult estimate)
{
bool found;
this.s0 = new ModelParameter(PopulateHelper.GetValue("S0", estimate.Names, estimate.Values, out found), this.s0.Description);
bool errors = RetrieveCurve(container.Context, false);
if (!errors)
{
PFunction rFunc = estimate.Objects[0] as PFunction;
PFunction rFuncDest = this.r.fVRef() as PFunction;
rFuncDest.Expr = rFunc.Expr;
PFunction qFunc = estimate.Objects[1] as PFunction;
PFunction qFuncDest = this.q.fVRef() as PFunction;
qFuncDest.Expr = qFunc.Expr;
//Calibrator assumes dividend yield is a step constant function, the simulation model must be coherent with that assumption.
qFuncDest.m_Function.iType = DVPLUtils.EInterpolationType.ZERO_ORDER_LEFT;
PFunction2D.PFunction2D localVolSrc = estimate.Objects[2] as PFunction2D.PFunction2D;
PFunction2D.PFunction2D localVolDest = this.localVol.fVRef() as PFunction2D.PFunction2D;
localVolDest.Expr = localVolSrc.Expr;
localVolDest.Interpolation = localVolSrc.Interpolation;
}
}
/// <summary>
/// Attempts a calibration through <see cref="SwaptionHW1OptimizationProblem"/>
/// using swaption matrices.
/// </summary>
/// <param name="data">The data to be used in order to perform the calibration.</param>
/// <param name="settings">The parameter is not used.</param>
/// <param name="controller">The controller which may be used to cancel the process.</param>
/// <returns>The results of the calibration.</returns>
public EstimationResult Estimate(List <object> data, IEstimationSettings settings = null, IController controller = null, Dictionary <string, object> properties = null)
{
InterestRateMarketData dataset = data[0] as InterestRateMarketData;
MatrixMarketData normalVol = null;
if (data.Count > 1)
{
normalVol = (MatrixMarketData)data[1];
}
PFunction zr = new PFunction(null);
// Loads the zero rate.
double[,] zrvalue = (double[, ])ArrayHelper.Concat(dataset.ZRMarketDates.ToArray(), dataset.ZRMarket.ToArray());
zr.Expr = zrvalue;
double deltak = dataset.SwaptionTenor;
Console.WriteLine("Swaption Tenor\t" + dataset.SwaptionTenor);
var swaptionsFiltering = settings as SwaptionsFiltering;
if (swaptionsFiltering == null)
{
swaptionsFiltering = new SwaptionsFiltering();//creates a default
}
//F stands for Full matrix
var optionMaturityF = normalVol != null ? normalVol.RowValues: dataset.OptionMaturity;
var swapDurationF = normalVol != null ? normalVol.ColumnValues: dataset.SwapDuration;
var swaptionsVolatilityF = normalVol != null ? normalVol.Values: dataset.SwaptionsVolatility;
int maturitiesCount = optionMaturityF.Count(x => x >= swaptionsFiltering.MinSwaptionMaturity && x <= swaptionsFiltering.MaxSwaptionMaturity);
int durationsCount = swapDurationF.Count(x => x >= swaptionsFiltering.MinSwapDuration && x <= swaptionsFiltering.MaxSwapDuration);
Console.WriteLine(string.Format("Calibrating on {0} swaptions prices [#maturiries x #durations]=[{1} x {2}]", maturitiesCount * durationsCount, maturitiesCount, durationsCount));
if (maturitiesCount * durationsCount == 0)
{
return(new EstimationResult("No swaptions satisfying criteria found, please relax filters"));
}
//reduced version
var swaptionsVolatility = new Matrix(maturitiesCount, durationsCount); // dataset.SwaptionsVolatility;
var optionMaturity = new Vector(maturitiesCount); // dataset.OptionMaturity;
var swapDuration = new Vector(durationsCount); // dataset.SwapDuration;
//Build filtered matrix and vectors
int fm = 0;
for (int m = 0; m < optionMaturityF.Length; m++)
{
int fd = 0;
if (optionMaturityF[m] >= swaptionsFiltering.MinSwaptionMaturity && optionMaturityF[m] <= swaptionsFiltering.MaxSwaptionMaturity)
{
for (int d = 0; d < swapDurationF.Length; d++)
{
if (swapDurationF[d] >= swaptionsFiltering.MinSwapDuration && swapDurationF[d] <= swaptionsFiltering.MaxSwapDuration)
{
swaptionsVolatility[fm, fd] = swaptionsVolatilityF[m, d];
swapDuration[fd] = swapDurationF[d];
fd++;
}
}
optionMaturity[fm] = optionMaturityF[m];
fm++;
}
}
var swbm = new SwaptionsBlackModel(zr, BlackModelFactory(zr));
Matrix fsr;
var blackSwaptionPrice = 1000.0 * swbm.SwaptionsSurfBM(optionMaturity, swapDuration, swaptionsVolatility, deltak, out fsr);
Console.WriteLine("Maturities\t" + optionMaturity);
Console.WriteLine("swapDuration\t" + swapDuration);
Console.WriteLine("SwaptionHWEstimator: Black model prices");
Console.WriteLine(blackSwaptionPrice);
SwaptionHW1 swhw1 = new SwaptionHW1(zr);
SwaptionHW1OptimizationProblem problem = new SwaptionHW1OptimizationProblem(swhw1, blackSwaptionPrice, optionMaturity, swapDuration, deltak);
IOptimizationAlgorithm solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 20;
o.MaxIter = 5;
o.Verbosity = 1;
o.controller = controller;
SolutionInfo solution = null;
Vector x0 = new Vector(new double[] { 0.1, 0.1 });
solution = solver.Minimize(problem, o, x0);
if (solution.errors)
{
return(new EstimationResult(solution.message));
}
o.epsilon = 10e-8;
o.h = 10e-8;
o.MaxIter = 1000;
// We can permit this, given it is fast.
o.accourate_numerical_derivatives = true;
if (solution != null)
{
solution = solver2.Minimize(problem, o, solution.x);
}
else
{
solution = solver2.Minimize(problem, o, x0);
}
if (solution.errors)
{
return(new EstimationResult(solution.message));
}
Console.WriteLine("Solution:");
Console.WriteLine(solution);
string[] names = new string[] { "Alpha", "Sigma" };
Console.WriteLine("SwaptionHWEstimator: hw model prices and error");
problem.Obj(solution.x, true);
EstimationResult result = new EstimationResult(names, solution.x);
result.ZRX = (double[])dataset.ZRMarketDates.ToArray();
result.ZRY = (double[])dataset.ZRMarket.ToArray();
double obj = problem.Obj(solution.x);
return(result);
}
private EstimationResult FairmatEstimate(CurveMarketData discountingCurve, CallPriceMarketData Hdataset)
{
EquityCalibrationData HCalData = new EquityCalibrationData(Hdataset, discountingCurve);
//HCalData.Setup(Hdataset, discountingCurve);
bool hasArbitrage = HCalData.HasArbitrageOpportunity(10e-2);
if (hasArbitrage)
Console.WriteLine("Market data contains arbitrage opportunity");
this.r = new DVPLDOM.PFunction(discountingCurve.Durations,discountingCurve.Values);
this.q = HCalData.dyFunc as PFunction;
//this.q.Expr = (double[,])ArrayHelper.Concat(HCalData.MaturityDY.ToArray(), HCalData.DividendYield.ToArray());
this.r.Parse(null);
this.q.Parse(null);
Vector locVolMat, locVolStr;
//IFunction fittedSurface = FitImplVolModel(Hdataset);
//Matrix locVolMatrix = LocVolMatrixFromImpliedVol(Hdataset, fittedSurface, out locVolMat, out locVolStr);
CallPriceSurface fittedSurface = CallPriceSurface.NoArbitrageSurface(HCalData);
Matrix locVolMatrix = LocVolMatrixFromCallPrices(Hdataset, fittedSurface, out locVolMat, out locVolStr);
Console.WriteLine(locVolMatrix);
// Create dupire outputs.
PFunction2D.PFunction2D localVol = new PFunction2D.PFunction2D(locVolMat, locVolStr, locVolMatrix);
localVol.Parse(null);
string[] names = new string[] { "S0" };
Vector param = new Vector(1);
param[0] = Hdataset.S0;
EstimationResult result = new EstimationResult(names, param);
//result.Objects = new object[3];
result.Objects = new object[4];
result.Objects[0] = this.r;
result.Objects[1] = this.q;
result.Objects[2] = localVol;
result.Objects[3] = fittedSurface;
//Console.WriteLine("r = " + HCalData.Rate.ToString());
//Console.WriteLine("q = " + HCalData.DividendYield.ToString());
return result;
}
public EstimationResult Estimate(IDictionary<string, string> runtimeParameters, EstimationResult previousStageResult, bool optimize)
{
var result = new EstimationResult(previousStageResult);
var optimized = Enumerable.Empty<EstimationResult.ParameterValue>();
if (optimize)
{
optimized = Optimize();
if (previousStageResult != null && previousStageResult.Parameters != null && previousStageResult.Parameters.Count > 0)
{
result.Parameters.AddRange(optimized);
}
else
{
result.Parameters = optimized.ToList();
}
}
foreach (var runtimeParameter in runtimeParameters)
{
if (!_values.ContainsKey(runtimeParameter.Key))
{
_values.Add(runtimeParameter);
}
}
result.CalculationTime = ComputeTime(previousStageResult != null ? previousStageResult.Time : 0);
result.Parameters.AddRange(
GetParameters().Where(p => optimized.All(op => op.Name != p.Name)).
Select(p =>
new EstimationResult.ParameterValue {
Name = p.Name,
InitialValue = GetParameterValue(p.Name),
NewValue = GetParameterValue(p.Name) })
);
foreach (var runtimeParameter in runtimeParameters)
{
_values.Remove(runtimeParameter.Key);
}
return result;
}
/// <summary>
/// Attempts a calibration through <see cref="PelsserCappletOptimizationProblem"/>
/// using caps matrices.
/// </summary>
/// <param name="data">The data to be used in order to perform the calibration.</param>
/// <param name="settings">The parameter is not used.</param>
/// <param name="controller">The controller which may be used to cancel the process.</param>
/// <returns>The results of the calibration.</returns>
public EstimationResult Estimate(List<object> data, IEstimationSettings settings = null, IController controller = null, Dictionary<string, object> properties = null)
{
InterestRateMarketData dataset = data[0] as InterestRateMarketData;
EstimationResult result;
if ((dataset.ZRMarket == null) || (dataset.CapVolatility == null))
{
result = new EstimationResult();
result.ErrorMessage = "Not enough data to calibrate.\n" +
"The estimator needs a ZRMarket and a CapVolatility " +
"defined inside InterestRateMarketData";
return result;
}
// Backup the dates
DateTime effectiveDate = DateTime.Now.Date;
DateTime valuationDate = DateTime.Now.Date;
if (Document.ActiveDocument != null)
{
effectiveDate = Document.ActiveDocument.ContractDate;
valuationDate = Document.ActiveDocument.SimulationStartDate;
}
// Creates the Context.
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
Function zr = new PFunction(null);
zr.VarName = "zr";
// Load the zr.
double[,] zrvalue = (double[,])ArrayHelper.Concat(dataset.ZRMarketDates.ToArray(), dataset.ZRMarket.ToArray());
zr.Expr = zrvalue;
prj.Symbols.Add(zr);
BlackModel bm = new BlackModel(zr);
double deltak = dataset.CapTenor;
Matrix capVol = dataset.CapVolatility;
Vector capMat = dataset.CapMaturity;
Vector capK = dataset.CapRate;
var preferences = settings as Fairmat.Calibration.CapVolatilityFiltering;
// Matrix calculated with black.
Matrix blackCaps = new Matrix(capMat.Length, capK.Length);
for (int m = 0; m < capMat.Length; m++)
{
for (int s = 0; s < capK.Length; s++)
{
bool skip = false;
if (preferences != null)
{
if (capK[s] < preferences.MinCapRate || capK[s] > preferences.MaxCapRate ||
capMat[m] < preferences.MinCapMaturity || capMat[m] > preferences.MaxCapMaturity)
{skip = true; }
}
if (capVol[m, s] == 0 || skip)
blackCaps[m, s] = 0;
else
blackCaps[m, s] = bm.Cap(capK[s], capVol[m, s], deltak, capMat[m]);
}
}
if (blackCaps.IsNAN())
{
Console.WriteLine("Black caps matrix has non real values:");
Console.WriteLine(blackCaps);
throw new Exception("Cannot calculate Black caps");
}
// Maturity goes from 0 to the last item with step deltaK.
Vector maturity = new Vector((int)(1.0 + capMat[capMat.Length - 1] / deltak));
for (int l = 0; l < maturity.Length; l++)
maturity[l] = deltak * l;
Vector fwd = new Vector(maturity.Length - 1);
for (int i = 0; i < fwd.Length; i++)
{
fwd[i] = bm.Fk(maturity[i + 1], deltak);
}
// Creates a default Pelsser model.
Pelsser.SquaredGaussianModel model = new Pelsser.SquaredGaussianModel();
model.a1 = (ModelParameter)0.014;
model.sigma1 = (ModelParameter)0.001;
model.zr = (ModelParameter)"@zr";
StochasticProcessExtendible iex = new StochasticProcessExtendible(prj, model);
prj.Processes.AddProcess(iex);
prj.Parse();
DateTime t0 = DateTime.Now;
Caplet cp = new Caplet();
PelsserCappletOptimizationProblem problem = new PelsserCappletOptimizationProblem(prj, cp, maturity, fwd, capK, deltak, capMat, blackCaps);
IOptimizationAlgorithm solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 35;
o.TargetCost = 0.0025;
o.MaxIter = 10;
o.Verbosity = Math.Max(1, Engine.Verbose);
o.controller = controller;
// Parallel evaluation is not supported for this calibration.
o.Parallel = false;
o.Debug = true;
SolutionInfo solution = null;
Vector x0 = (Vector)new double[] { 0.1, 0.1 };
solution = solver.Minimize(problem, o, x0);
if (solution.errors)
return new EstimationResult(solution.message);
o.epsilon = 10e-7;
o.h = 10e-7;
o.MaxIter = 1000;
o.Debug = true;
o.Verbosity = Math.Max(1, Engine.Verbose);
if (solution != null)
solution = solver2.Minimize(problem, o, solution.x);
else
solution = solver2.Minimize(problem, o, x0);
if (solution.errors)
return new EstimationResult(solution.message);
Console.WriteLine(solution);
string[] names = new string[] { "alpha1", "sigma1" };
result = new EstimationResult(names, solution.x);
result.ZRX = (double[])dataset.ZRMarketDates.ToArray();
result.ZRY = (double[])dataset.ZRMarket.ToArray();
result.Objects = new object[1];
result.Objects[0] = solution.obj;
//result.Fit = solution.obj;//Uncomment in 1.6
// Restore the dates
if (Document.ActiveDocument != null)
{
Document.ActiveDocument.ContractDate = effectiveDate;
Document.ActiveDocument.SimulationStartDate = valuationDate;
}
return result;
}
private static Vector Test(int nm, int nk, double q, double s0, double r, double t, double theta, double sigma, double nu)
{
// Simulate synthetic data.
Vector m = new Vector(nm);
Vector k = new Vector(nk);
Matrix cp = new Matrix(nm, nk);
Random rand = new Random();
for (int i = 0; i < nm; i++)
{
m[i] = 0.01 + rand.NextDouble() * 0.99;
}
for (int i = 0; i < nk; i++)
{
k[i] = 60 + rand.NextDouble() * 90;
}
for (int i = 0; i < nm; i++)
{
for (int j = 0; j < nk; j++)
{
cp[i, j] = VarianceGammaOptionsCalibration.VGCall(theta, sigma, nu, m[i], k[j], q, s0, r);
}
}
Console.WriteLine("Benchmark value");
Console.WriteLine(new Vector()
{
theta, sigma, nu
});
Console.WriteLine("Call prices");
Console.WriteLine(cp);
// VGDiff at optimum.
double fopt = VarianceGammaOptimizationProblem.VGDiff(new Vector()
{
theta, sigma, nu
}, q, s0, k, r, cp, m);
Console.WriteLine("fopt");
Console.WriteLine(fopt);
VarianceGammaOptionsCalibration c = new VarianceGammaOptionsCalibration();
List <object> marketData = new List <object>();
var espmd = new EquitySpotMarketData();
espmd.Price = s0;
espmd.RiskFreeRate = r;
espmd.DividendYield = q;
var cpmd = new CallPriceMarketData();
cpmd.Strike = k;
cpmd.Maturity = m;
cpmd.CallPrice = cp;
var dc = new DiscountingCurveMarketData();
dc.Durations = new Vector()
{
0
};
dc.Values = new Vector()
{
r
};
marketData.Add(espmd);
marketData.Add(cpmd);
marketData.Add(dc);
EstimationResult res = c.Estimate(marketData, null);
return((Vector)res.Values);
}
private EstimationResult QuantLibEstimate(CurveMarketData discoutingCurve, CallPriceMarketData Hdataset)
{
EquityCalibrationData HCalData = new EquityCalibrationData(Hdataset, discoutingCurve);
bool hasArbitrage = HCalData.HasArbitrageOpportunity(10e-2);
if (hasArbitrage)
Console.WriteLine("Market data contains arbitrage opportunity");
this.r = new DVPLDOM.PFunction(discoutingCurve.Durations,discoutingCurve.Values);
this.q = HCalData.dyFunc as PFunction;
//this.r.Parse(null);
//this.q.Parse(null);
Hdataset.Volatility = new Matrix(Hdataset.CallPrice.R, Hdataset.CallPrice.C);
for (int i = 0; i < Hdataset.Volatility.R; i++)
{
double m=Hdataset.Maturity[i];
for (int j = 0; j < Hdataset.Volatility.C; j++)
{
if (Hdataset.CallPrice[i, j] > 0)
{
var bs = new Fairmat.Finance.BlackScholes(r.Evaluate(m), Hdataset.S0, Hdataset.Strike[j], 0, m, q.Evaluate(m));
//Hdataset.Volatility[i, j] = Hdataset.Volatility[i, j] * Hdataset.Volatility[i, j] * Hdataset.Maturity[i];
//Hdataset.Volatility[i, j] = bs.ImpliedCallVolatility(Hdataset.CallPrice[i, j]);
}
}
}
Console.WriteLine(Hdataset.Volatility);
IFunction impVol = FitImplVolModel(Hdataset);
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
prj.Symbols.Add(impVol);
// doc.WriteToXMLFile("impVol.fair");
int nmat = calibrationSettings.LocalVolatilityMaturities;
int nstrike = calibrationSettings.LocalVolatilityStrikes;
double lastMat = Hdataset.Maturity[SymbolicIntervalExtremes.End];
double lastStr = Hdataset.Strike[SymbolicIntervalExtremes.End];
Vector locVolMat = Vector.Linspace(Hdataset.Maturity[0], lastMat, nmat);
Vector locVolStr = Vector.Linspace(Hdataset.Strike[0], lastStr, nstrike);
Matrix locVolMatrix = new Matrix(nmat, nstrike);
double t, dt, forwardValue, y, dy, strike, strikep, strikem, w, wp, wm, dwdy;
double d2wdy2, den1, den2, den3, strikept, strikemt, wpt, wmt, dwdt;
Integrate integrate = new Integrate(this);
for (int i = 0; i < nmat; i++)
{
t = locVolMat[i];
forwardValue = Hdataset.S0 * Math.Exp(integrate.AdaptLobatto(0.0, t));
for (int j = 0; j < nstrike; j++)
{
strike = locVolStr[j];
y = Math.Log(strike / forwardValue);
dy = ((Math.Abs(y) > 0.001) ? y * 0.0001 : 0.000001);
// strike derivative
strikep = strike * Math.Exp(dy);
strikem = strike / Math.Exp(dy);
w = impVol.Evaluate(t, strike);
wp = impVol.Evaluate(t, strikep);
wm = impVol.Evaluate(t, strikem);
dwdy = (wp - wm) / (2.0 * dy);
d2wdy2 = (wp - 2.0 * w + wm) / (dy * dy);
// time derivative
if (t == 0.0)
{
dt = 0.0001;
strikept = strike * Math.Exp(integrate.AdaptLobatto(0.0, t + dt));
wpt = impVol.Evaluate(t + dt, strikept);
// if (wpt < w)
// Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t, t + dt);
dwdt = (wpt - w) / dt;
}
else
{
dt = Math.Min(0.0001, t / 2.0);
strikept = strike * Math.Exp(integrate.AdaptLobatto(t, t + dt));
strikemt = strike * Math.Exp(-integrate.AdaptLobatto(t - dt, t));
wpt = impVol.Evaluate(t + dt, strikept);
wmt = impVol.Evaluate(t + dt, strikemt);
//if (wpt < w)
// Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t, t + dt);
//if (w < wmt)
// Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t-dt, t);
dwdt = (wpt - wmt) / (2.0 * dt);
}
if (dwdy == 0.0 && d2wdy2 == 0.0)
locVolMatrix[i, j] = Math.Sqrt(dwdt);
else
{
den1 = 1.0 - y / w * dwdy;
den2 = 0.25 * (-0.25 - 1.0 / w + y * y / w / w) * dwdy * dwdy;
den3 = 0.5 * d2wdy2;
locVolMatrix[i, j] = dwdt / (den1 + den2 + den3);
//if (locVolMatrix[i,j] < 0.0)
// Console.WriteLine("Negative local vol^2 at strike {0} and time {1}; " +
// "Black vol surface is not smooth enought.", strike, t);
}
}
}
// Create dupire outputs.
Console.WriteLine(locVolMat);
PFunction2D.PFunction2D localVol = new PFunction2D.PFunction2D(locVolMat, locVolStr, locVolMatrix);
localVol.Parse(null);
string[] names = new string[] { "S0" };
Vector param = new Vector(1);
param[0] = Hdataset.S0;
EstimationResult result = new EstimationResult(names, param);
//result.Objects = new object[3];
result.Objects = new object[4];
result.Objects[0] = this.r;
result.Objects[1] = this.q;
result.Objects[2] = localVol;
result.Objects[3] = impVol;
//Console.WriteLine("r = " + HCalData.Rate.ToString());
//Console.WriteLine("q = " + HCalData.DividendYield.ToString());
return result;
}
public void TestCalibration()
{
InterestRateMarketData IData = InterestRateMarketData.FromFile("../../TestData/IRMD-sample.xml");
CallPriceMarketData HData = CallPriceMarketData.FromFile("../../TestData/CallData-sample.xml");
//InterestRateMarketData IData = InterestRateMarketData.FromFile("../../../EquityModels.Tests/TestData/IRMD-EU-30102012-close.xml");
//CallPriceMarketData HData = CallPriceMarketData.FromFile("../../../EquityModels.Tests/TestData/30102012-SX5E_Index-HestonData.xml");
//CallPriceMarketData HData = ObjectSerialization.ReadFromXMLFile("../../../EquityModels.Tests/TestData/FTSE.xml") as CallPriceMarketData;
List <object> l = new List <object>();
l.Add(IData.DiscountingCurve);
l.Add(HData);
DupireEstimator DE = new DupireEstimator();
DupireCalibrationSettings settings = new DupireCalibrationSettings();
settings.LocalVolatilityCalculation = LocalVolatilityCalculation.Method1;
//settings.LocalVolatilityCalculation = LocalVolatilityCalculation.QuantLib;
EstimationResult res = DE.Estimate(l, settings);
//int nmat = HData.Maturity.Length;
//int nstrike = HData.Strike.Length;
int i = 5; // Maturity.
int j = 4; // Strike.
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 10000;
int n_steps = 500;
double strike = HData.Strike[j];
//double volatility = HData.Volatility[i, j];
/*
* PFunction2D.PFunction2D impvolfunc = new PFunction2D.PFunction2D(rov);
* impvolfunc = res.Objects[3] as PFunction2D.PFunction2D;
* impvolfunc.VarName = "impvol";
* rov.Symbols.Add(impvolfunc);
* double volatility = impvolfunc.Evaluate(HData.Maturity[i], HData.Strike[j]);
*/
double volatility = 0.2;
double maturity = HData.Maturity[i];
ModelParameter Pstrike = new ModelParameter(strike, string.Empty, "strike");
rov.Symbols.Add(Pstrike);
AFunction payoff = new AFunction(rov);
payoff.VarName = "payoff";
payoff.m_IndependentVariables = 1;
payoff.m_Value = (RightValue)("max(x1 - strike ; 0)");
rov.Symbols.Add(payoff);
bool found;
double S0 = PopulateHelper.GetValue("S0", res.Names, res.Values, out found);
ModelParameter PS0 = new ModelParameter(S0, string.Empty, "S0");
rov.Symbols.Add(PS0);
PFunction rfunc = new PFunction(rov);
rfunc = res.Objects[0] as PFunction;
rfunc.VarName = "r";
rov.Symbols.Add(rfunc);
PFunction qfunc = new PFunction(rov);
qfunc = res.Objects[1] as PFunction;
qfunc.VarName = "q";
rov.Symbols.Add(qfunc);
PFunction2D.PFunction2D volfunc = new PFunction2D.PFunction2D(rov);
volfunc = res.Objects[2] as PFunction2D.PFunction2D;
volfunc.VarName = "localvol";
rov.Symbols.Add(volfunc);
DupireProcess process = new DupireProcess();
process.s0 = (ModelParameter)"S0";
process.r = (ModelParameter)"@r";
process.q = (ModelParameter)"@q";
process.localVol = (ModelParameter)"@localvol";
double rate = rfunc.Evaluate(maturity);
double dy = qfunc.Evaluate(maturity);
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.RiskFree;
rfi.m_deterministicRF = rate;
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "payoff(v1)";
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity;
op.PayoffInfo.European = true;
rov.Map.Root = op;
rov.NMethods.Technology = ETechType.T_SIMULATION;
rov.NMethods.PathsNumber = n_sim;
rov.NMethods.SimulationSteps = n_steps;
ROVSolver solver = new ROVSolver();
solver.BindToProject(rov);
solver.DoValuation(-1);
if (rov.HasErrors)
{
rov.DisplayErrors();
}
Assert.IsFalse(rov.HasErrors);
ResultItem price = rov.m_ResultList[0] as ResultItem;
double samplePrice = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim);
Console.WriteLine("Surf = " + volfunc.Expr);
// Calculation of the theoretical value of the call.
double theoreticalPrice = BlackScholes.Call(rate, S0, strike, volatility, maturity, dy);
Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
doc.WriteToXMLFile("Dupire.fair");
Assert.LessOrEqual(Math.Abs(theoreticalPrice - samplePrice), tol);
}
protected virtual EstimationResult BuildEstimate(Scalar spotPrice, CurveMarketData interestDataSet, CallPriceMarketData callDataSet, EquityCalibrationData equityCalData, SolutionInfo solution)
{
string[] names = new string[] { "S0", "kappa", "theta", "sigma", "rho", "V0" };
Vector param = new Vector(6);
param[0] = spotPrice.Value;
param[Range.New(1, 5)] = solution.x;
var result = new EstimationResult(names, param);
// In the following the two function describing the ZR and dividend yields are created
//Matrix zerorate = new Matrix(interestDataSet.Durations.Length, 2);
//zerorate[Range.All, 0] = interestDataSet.Durations;
//zerorate[Range.All, 1] = interestDataSet.Values;
//Matrix dividendYield = new Matrix(equityCalData.MaturityDY.Length, 2);
//dividendYield[Range.All, 0] = equityCalData.MaturityDY;
//dividendYield[Range.All, 1] = equityCalData.DividendYield;
Matrix zerorate = new Matrix((equityCalData.zrFunc as PFunction).Expr);
//Matrix dividendYield = new Matrix((equityCalData.dyFunc as PFunction).Expr);
Matrix dividendYield = ToMatrix(IstantaneousDividendYield(equityCalData));
result.Objects = new object[2];
result.Objects[0] = zerorate;
result.Objects[1] = dividendYield;
result.Fit = solution.obj;
Console.WriteLine(result);
return result;
}
